We assess the power of forward guidance - promises about future interest rates - as a monetary tool in a liquidity trap using a quantitative incomplete-markets model. Our results suggest the effects of forward guidance are negligible. A commitment to keep future nominal interest rates low for a few quarters-although macro indicators suggest otherwise-has only trivial effects on current output and employment. We explain theoretically why in complete markets models forward guidance is powerful-generating a "forward guidance puzzle"-and why this puzzle disappears in our model. We also clarify theoretically ambiguous conclusions from previous research about the effectiveness of forward guidance in incomplete and complete markets models.